How do I determine my web server's outgoing IP address?

How do I determine my web server's outgoing IP address? I don't have access to the server itself, but I can run an ASP script on it. I want to register to use an API, but the API requires that I register the IP address that the requests will be coming from. This is a lot harder for me to figure out than I thought it would be.

you will need setup a DNS address on internet ie API.companyname.com
Then set an IP address that is static on the internet that will point to this IP ie IP of your firewall.
Your firewall can then pass any web requests to your server internally when setting up a rule.